In particular in the field of electronics production, printed circuit boards or assemblies to be produced are manufactured on SMT component fitting lines by means of surface mounting (surface mounted technology, SMT). A manufacturer of SMT component fitting machines and systems with the product name SIPLACE is the ASM company (http://www.siplace.com/en/Home), for example.
On account of technical restrictions, not every assembly can be produced on every component fitting line, however. The assemblies for the most part also have different production times on the component fitting lines. Also, the maximum production time capacities of the component fitting lines cannot be exceeded.
The assignment of assemblies to component fitting lines of a component fitting system is usually made manually or semiautomatically, based on empirical values or heuristics.
Since the planning horizon during production is for the most part medium-term, there are uncertainties with regard to the future numbers of items of the different assembly types. This can lead to undesirably large fluctuations in the utilization levels/production times of the component fitting lines. Therefore, it is desirable in practice to avoid assembly line assignments that mean that particularly high production time fluctuations can arise for individual lines. This can result in the applicable lines often running above capacity or below capacity.
In the case of one possible use of mathematical optimization methods, linear optimization methods are possible. Linear optimization is concerned with the optimization of linear target functions over a set limited by linear equations and in equations. It is the basis of the solution methods of (mixed) integer linear optimization. What is known as a solver is a group designation for specific mathematical computer programs that can solve mathematical problems numerically. In connection with MIP (mixed integer linear programming), standard solvers such as e.g. CPLEX or Gurobi can be used for small IP programs (integer optimization models). Conceivable small IP programs are instances having two lines, 181 assemblies and 839 component types, for example. For larger instances, standard solvers such as CPLEX can give rise to problems for solving this more complex problem.
U.S. Pat. No. 6,829,514 B2 proposes using mixed integer linear programming during production for electronic assemblies to optimize individual production lines.
DE 198 34 620 A1 relates to a method for ascertaining an upgrade for a mix of different assembly types in a component fitting line.
DE 10 2011 076 565 B4, WO 2014/005741 A1, WO 2014/005743 A1 and WO 2014/005744 A1 disclose methods that are examples of optimization methods by means of MIP for assignments of assemblies to component fitting lines.
DE 10 2011 076 565 B4 especially discloses a method for assigning printed circuit boards to component fitting lines for fitting the printed circuit boards with components, which achieves the lowest possible component variance and the most optimum possible production time under prescribed constraints. In this case, the component variance is determined as a sum of the numbers of component types needed on the component fitting lines.
An equipment family is determined as a set of assemblies that can be fitted with components on a component fitting line without changing the set of component types kept on the component fitting line for component fitting. The set of component types kept on the component fitting line is also called equipment. Usually, a component fitting line has more assemblies assigned to it than an equipment family can comprise, since it is not possible for any number of component types to be kept on the component fitting line. The component fitting line is therefore occasionally subjected to a change of equipment, which involves the equipment for a first equipment family being changed for the equipment for a second equipment family. The rarer these equipment changes are, the less time consuming the operation of the component fitting system can be. The total number of equipment families used in the component fitting system may be a more realistic quality indicator than, by way of example, the component variance of a component fitting line. The component variance of a component fitting line is given by the number of different component types whose components are to be fitted to one of the assemblies assigned to the component fitting line. The method known from DE 10 2011 076 565 B4 can therefore determine assignments of assemblies to component fitting lines that allow an improved utilization level for the overall component fitting system.
In order to restrict maximum production time fluctuations for the individual lines or to minimize them as far as possible, further improvements are needed in the IP model.
To be able to obtain solutions for larger instances or more complex problems at all or even in optimized fashion, a good or precise selection of parameters in the IP model or IP program with the restrictions to be applied or the user-defined presets is fundamental.